Kidney stone classification from endoscopic images is critical for personalized treatment and recurrence prevention. While convolutional neural networks (CNNs) have shown promise in this task, their limited ability to capture long-range dependencies can hinder performance under variable imaging conditions. This study presents a comparative analysis between Vision Transformers (ViTs) and CNN-based models, evaluating their performance on two ex vivo datasets comprising CCD camera and flexible ureteroscope images. The ViT-base model pretrained on ImageNet-21k consistently outperformed a ResNet50 baseline across multiple imaging conditions. For instance, in the most visually complex subset (Section patches from endoscopic images), the ViT model achieved 95.2% accuracy and 95.1% F1-score, compared to 64.5% and 59.3% with ResNet50. In the mixed-view subset from CCD-camera images, ViT reached 87.1% accuracy versus 78.4% with CNN. These improvements extend across precision and recall as well. The results demonstrate that ViT-based architectures provide superior classification performance and offer a scalable alternative to conventional CNNs for kidney stone image analysis.